Answer:
So, this triangle PQR can be broken into two right triangles, PNQ and PNR, with legs PQ = 39, PN =15, and QN = ? and PR = 17, PN = 15, and NR =? respectively.
Let's solve for what is easier first:
Since we know that 5-15-17 is a Pythagorean triplet, we can infer that NR is 5....like I said earlier, it is a right triangle, so this guess holds true.
Here comes the interesting part:
Now, we have one part of QR, which is QN.
The other part can be solved by using the Pythagorean theorem.
It is (39^2-15^2)^(1/2)..which gives you 36, the square root of 1296, which happens to be the difference between the squares of 15 and 39.
SO, QR = QN + NR
5+36 = 41
QR = 41.
Hope this helps!
Answer:
Answer 24 cm^3
Step-by-step explanation:
If the dimensions are 1/2 the volume is 1/8 the original volume. There are 2 ways to do this. I'm going to choose the most straight forward.
Formula
V = L * w * h
Givens
L = 6
w = 8
h = 4
Solution
V_original = 6 * 8 * 4 = 192
V_half = 3 * 4 * 2 = 24
V_original / V_half = 192/24 = 8/1
So the other way around (V_half/V_original) = 1/8
Answer:
[1. 10.5] [2. 8.4] [3. 7.7]
Step-by-step explanation:
9.8 divided by 7 will give you the unit rate which each unit adds up by.
Answer:
So here is the answer to your question by using the formulae of compound amount.
Initial price( P) = $5000
Interest rate( R) = 2% pa
Time ( T) = 30 years
Compound amount (CA)=?
We have
CA=P(1+R/100)^T
=5000(1+2/100)^30
=$9056.807921
=$9057(Approx)
Thus, the money will be $9057 after 30 years.
Answer:
There were 61 bagels and 23 coffee sold
Step-by-step explanation:
Let us solve the question
∵ The number of bagels and coffee sold by a bagel shop yesterday
can be modeled using the equation b + c = 84
∴ b + c = 84 ⇒ (1)
∵ Their sales for the same day can be modeled using the equation
2b + c = 145
∴ 2b + c = 145 ⇒ (2)
Let us solve the system of equations using substitution
→ Subtract the two sides of equation (1) by b to find c in terms of b
∵ b - b + c = 84 - b
∴ c = 84 - b ⇒ (3)
→ Substitute c in equation (2) by equation (3)
∵ 2b + 84 - b = 145
→ Add the like terms on the left side
∴ (2b - b) + 84 = 145
∴ b + 84 = 145
→ Subtract 84 from both sides
∵ b + 84 - 84 = 145 - 84
∴ b = 61
→ Substitute the value of b in equation (3) to find c
∵ c = 84 - 61
∴ c = 23
∴ There were 61 bagels and 23 coffee sold.
